Stable ergodicity of skew products of one-dimensional hyperbolic flows

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1999, 5(4): 897-904. doi: 10.3934/dcds.1999.5.897

Stable ergodicity of skew products of one-dimensional hyperbolic flows

1.	Department of Mathematics, University of Manchester, Oxford Road, Manchester M13 9PL

Received January 1999 Revised June 1999 Published July 1999

Abstract
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We consider hyperbolic flows on one dimensional basic sets. Any such flow is conjugate to a suspension of a shift of finite type. We consider compact Lie group skew-products of such symbolic flows and prove that they are stably ergodic and stably mixing, within certain naturally defined function spaces.

Keywords: skew product, symbolic flow, Hyperbolic flow, stable ergodicity..

Mathematics Subject Classification: Primary: 58F1.

Citation: C.P. Walkden. Stable ergodicity of skew products of one-dimensional hyperbolic flows. Discrete & Continuous Dynamical Systems - A, 1999, 5 (4) : 897-904. doi: 10.3934/dcds.1999.5.897

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